Only substance is, according to Spinoza, conceived through itself. Modes are conceived through their relations to other modes and, ultimately, through substance. So existence is of the essence of substance, but existence is not of the essence of modes. — John
What remains unclear to me is what it means to say that the principle of identity does not apply to something. Zalamea helpfully formalizes the principles of vagueness and generality on page 21 of his paper; he describes them as failures of distribution of the principles of contradiction and excluded middle, respectively. Is there an analogous way to formalize the principle of identity and/or its failure, which would show what you have in mind here? — aletheist
But in what sense, then, is this distinctive of 2ns, in the same way that the inapplicability of the principles of contradiction and excluded middle are distinctive of vageness/1ns and generality/3ns, respectively? — aletheist
Yes, Spinoza's concept of substance is contradictory to Aristotle's concept. Spinoza denies that there can be many finite substances and contends that there can be only one infinite substance. — John
I note you never got around to talking about the fate of the point but instead wandered off to talk about something else. — apokrisis
Take the rationals, and make a cut at <2. 2 stays on on side, all the numbers less than 2 on the other. One side contains 2, while the other might approach 2, but by the very fact of the cut, never reaches it. — Banno
Anyway 2ns would stand in relation to the law of identity as this same kind of protest - I am not constrained by that constraint which is said to be required to produce the brutely particular. — apokrisis
A sign is objectively general, in so far as, leaving its effective interpretation indeterminate, it surrenders to the interpreter the right of completing the determination for himself. "Man is mortal." "What man?" "Any man you like." A sign is objectively vague, in so far as, leaving its interpretation more or less indeterminate, it reserves for some other possible sign or experience the function of completing the determination. "This month," says the almanac-oracle, "a great event is to happen." "What event?" "Oh, we shall see. The almanac doesn't tell that." — CP 5.505, c. 1905
The general might be defined as that to which the principle of excluded middle does not apply. A triangle in general is not isosceles nor equilateral; nor is a triangle in general scalene. The vague might be defined as that to which the principle of contradiction does not apply. For it is false neither that an animal (in a vague sense) is male, nor that an animal is female. — CP 5.505, c. 1905
Would "contextuality" be a good descriptive term for this characteristic, as the second member of a trichotomy with vagueness and generality? What about "substance" to go along with matter and form? — aletheist
As a first cut: If x is contextual, then it is not necessarily true that under all circumstances, x = x. — aletheist
No, the two concepts aren't contradictory in any way. They are actually compatible. It is true that Aristotle means something different by Substance than Spinoza, however, the two concepts (their meanings) are not contradictory, but complementary. Substance in Spinoza is that which cannot be conceived as not existing, and which must be conceived through itself. There is only one element of Aristotle's metaphysics which fits this description - and there is only ONE of them - the Prime Mover. So Substance in Spinoza is NOT Substance in Aristotle, but rather Prime Mover. Hence the two definitions of Substance aren't even incompatible to begin with.Yes, Spinoza's concept of substance is contradictory to Aristotle's concept. Spinoza denies that there can be many finite substances and contends that there can be only one infinite substance. — John
I don't think it is essential to arrive at one perfect word. — apokrisis
But if vagueness is the best term for 1ns, and generality the best for 3ns, then another term for 2ns (after hierarchy theory) would be specificity. — apokrisis
I mean 2ns looks the most like the regular reductionist notion of the atomistically and mechanically determinate - in simply being Newtonian action and reaction. — apokrisis
The logical atom, or term not capable of logical division, must be one of which every predicate may be universally affirmed or denied ... Such a term can be realized neither in thought nor in sense ... In thought, an absolutely determinate term cannot be realized, because, not being given by sense, such a concept would have to be formed by synthesis, and there would be no end to the synthesis because there is no limit to the number of possible predicates. A logical atom, then, like a point in space, would involve for its precise determination an endless process. We can only say, in a general way, that a term, however determinate, may be made more determinate still, but not that it can be made absolutely determinate. Such a term as "the second Philip of Macedon" is still capable of logical division - into Philip drunk and Philip sober, for example; but we call it individual because that which is denoted by it is in only one place at one time. It is a term not absolutely indivisible, but indivisible as long as we neglect differences of time and the differences which accompany them. Such differences we habitually disregard in the logical division of substances. In the division of relations, etc., we do not, of course, disregard these differences, but we disregard some others. There is nothing to prevent almost any sort of difference from being conventionally neglected in some discourse ... This distinction between the absolutely indivisible and that which is one in number from a particular point of view is shadowed forth in the two words individual {to atomon} and singular (to kath' hekaston); but as those who have used the word individual have not been aware that absolute individuality is merely ideal, it has come to be used in a more general sense. — CP 3.63, 1870
"That is why I said the contradiction lies in the genesis of specificity. Peirceanism says it is a contextual deal. The laws of thought say it is brutely tautological. — "apokrisis
Or x = not not-x is true. That employs the context to derive the specificity via a dichotomy. — apokrisis
Indeed, the actual, the given, the present, the instant, are no more than ideal limits: limits of possibility neighbourhoods which contain those actuality marks, those points impossible to be drawn, those fleeting presents, those impalpable instants.
No, the two concepts aren't contradictory in any way. — Agustino
Another way to put it is that if generality and vagueness are real yet not actual, then the actual would be the not real. — apokrisis
Existence, then, is a special mode of reality, which, whatever other characteristics it possesses, has that of being absolutely determinate. Reality, in its turn, is a special mode of being, the characteristic of which is that things that are real are whatever they really are, independently of any assertion about them. — CP 6.349, 1902
Existence can approach but not reach the perfection of discontinuous actualisation that the principle of identity demands. — apokrisis
The first requires determinacy with respect to every general character, and thus - as he wrote elsewhere (see below) - can only be an ideal limit; while the second makes individuality a matter of reaction, and therefore existence. — aletheist
Peirce's definition of "real" is that which has characters regardless of what anyone thinks about it. — aletheist
Both effectively deny the identity of indiscernibles, the first by virtue of the different "hecceities" that two distinct individuals must have, and the second because no two reacting things can have the same spatial (or, I would add, temporal) relations.
The latter is what I had in mind when I suggested as an example of contextuality, "This object from one point of view, or at one time and place, is not the same as this object from another point of view, or at another time and place." — aletheist
There is nothing to prevent almost any sort of difference from being conventionally neglected in some discourse ... — CP 3.63, 1870
This distinction between the absolutely indivisible and that which is one in number from a particular point of view is shadowed forth in the two words individual {to atomon} and singular (to kath' hekaston); but as those who have used the word individual have not been aware that absolute individuality is merely ideal, it has come to be used in a more general sense. — CP 3.63, 1870
This is the basis on which I have elsewhere suggested "extreme realism" as the view that reality consists entirely of generals, or at least that everything real is general to some degree. — aletheist
As a second cut: If x is contextual, then it is not necessarily true that under all circumstances, x = ¬¬x. — aletheist
Hence if one or the other does not apply, negation is left undefined. — aletheist
If we are now talking cosmology, it is the Universe that is indifferent to any difference that doesn't make a difference in being beyond the needs of its genenralised purpose. — apokrisis
1ns can't be the true initial conditions of existence as Peirce's own logic makes necessary. — apokrisis
So again, 2ns in Peirceanism is about the emergence of crisp possibility or determinate degrees of freedom. — apokrisis
This of course is what I deny. There is only relativity, never the absolute. — apokrisis
X is being made its own context. That is the tautology here. The assertion is being made that the context is crisply existent too - thus bringing out that which Peirceanism would seek to deny. — apokrisis
The upshot then is that the statement is true only to the degree that either term is true. — apokrisis
If x is contextual, then it is not necessarily true that _____.
A sign is objectively contextual, in so far as, leaving its interpretation indeterminate, it relies on some aspect of the actual situation to complete the determination. "That house is on fire." "What house?" "That one over there."
The contextual might be defined as that to which the principle of identity does not apply. This object from one point of view, or at one time and place, is not the same as this object from another point of view, or at another time and place.
But where the reductionist thinks that the differences that make a difference are atomistically unbounded - there is no reason why we could ever in principle cease the pursuit of further detail, chase down the last decimal of the expansion of pi until we are exhausted - the Peircean system offers principled relief. We can stop when the differences cease to matter to our over-riding purpose. — apokrisis
Which statement? Which terms? I want to make sure that I clearly understand what you are saying here. Also, how would you fill in the blank with some formalized version of the principle of identity? — aletheist
While I am at it, do you agree or disagree with my other "first cut" definitions of "contextual" that parallel what Peirce wrote about "vague" and "general"? — aletheist
Which is what, in your view? — aletheist
This is one point at which I am having consistent trouble tracking with you. I understand 2ns in Peirceanism to be about brute reaction/resistance, the absence of freedom (1ns) and reason/purpose (3ns). — aletheist
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